Untwisting number and Blanchfield pairings
Maciej Borodzik
TL;DR
This paper explores the use of Blanchfield forms to analyze knots that can be unknotted with a single specific move, providing new insights into knot simplification techniques.
Contribution
It introduces a novel application of Blanchfield pairings to characterize knots reducible by a single -move, advancing knot theory methods.
Findings
Blanchfield forms effectively detect knots unknottable by one move.
New criteria for -move unknotting using algebraic invariants.
Enhanced understanding of knot simplification processes.
Abstract
In this note we use Blanchfield forms to study knots that can be turned into an unknot using a single move.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Rings, Modules, and Algebras